Converting bags and marbles into equations

In this lesson we will begin by solving a puzzle using bags of marbles. Then we will write the algebraic equation represented by the bags and marbles and show that the solution satisfies the equation.

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First, let's solve the following puzzle to determine the number of marbles in each bag.

One bag and nine marbles on the left weigh the same as four bags and three marbles on the right.How many marbles are in each bag?

To solve this problem, first remove one marble bag from each side, then remove three marbles from each side, which leaves three marble bags on the right and six marbles on the left. Now it is easy to see that each marble bag contains two marbles.

The bags and marbles are a model to make it easier for you to think about algebraic equations. Since the two sides of the balance weigh the same amount, we can write an equation to represent this situation.